Question: Solve for $x$ and $y$ using elimination. ${2x+5y = 51}$ ${-2x-4y = -42}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $2x$ and $-2x$ cancel out. ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {2x+5y = 51}\thinspace$ to find $x$ ${2x + 5}{(9)}{= 51}$ $2x+45 = 51$ $2x+45{-45} = 51{-45}$ $2x = 6$ $\dfrac{2x}{{2}} = \dfrac{6}{{2}}$ ${x = 3}$ You can also plug ${y = 9}$ into $\thinspace {-2x-4y = -42}\thinspace$ and get the same answer for $x$ : ${-2x - 4}{(9)}{= -42}$ ${x = 3}$